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A052878
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E.g.f.: log((1-x)/(1-3*x+x^2)).
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1
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0, 2, 6, 34, 276, 2928, 38520, 606240, 11118240, 232928640, 5488922880, 143707737600, 4138613740800, 130021152307200, 4425207423436800, 162194949242726400, 6369480464675328000, 266808295408951296000, 11874724735152254976000, 559591803705456377856000
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OFFSET
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0,2
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COMMENTS
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Previous name was: A simple grammar.
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LINKS
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FORMULA
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Recurrence: {a(1)=2, a(2)=6, a(3)=34, (-n^3-2*n-3*n^2)*a(n)+(4*n^2+12*n+8)*a(n+1)+(-4*n-8)*a(n+2)+a(n+3)}
For n > 0, a(n) = (n-1)! * (phi^(2*n) + 1/phi^(2*n) - 1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 06 2019
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MAPLE
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spec := [S, {B=Sequence(Z, 1 <= card), C=Union(Z, B), S=Cycle(C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
with(combinat):
0, seq( (fibonacci(2*n+1)+fibonacci(2*n-1)-1) * (n-1)!, n=1..20); # Mark van Hoeij, May 29 2013
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PROG
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(PARI) x='x+O('x^66); concat([0], Vec(serlaplace(log(-(-1+x)/(1-3*x+x^2))))) \\ Joerg Arndt, May 29 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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